For the inverse variation equation [tex]xy=k[/tex], what is the constant of variation, [tex]k[/tex], when [tex]x=-3[/tex] and [tex]y=-2[/tex] ?
A. -6
B. -[tex]\frac{2}{3}[/tex]
C. [tex]\frac{3}{2}[/tex]
D. 6

The constant of variation k for the given values x = -3 and y = -2 in the equation xy = k is 6. Therefore, the selected option is D. 6.
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Answered by Anonymous | 2025-07-04

Substitute the given values x = − 3 and y = − 2 into the inverse variation equation x y = k .
Calculate the product of x and y : ( − 3 ) × ( − 2 ) = 6 .
Determine the constant of variation: k = 6 .
State the final answer: 6 ​ .

Explanation

Understanding the Problem We are given the inverse variation equation x y = k , where k is the constant of variation. We are also given that x = − 3 and y = − 2 . Our goal is to find the value of k .

Substituting the Values To find the constant of variation k , we substitute the given values of x and y into the equation x y = k . So, we have ( − 3 ) × ( − 2 ) = k .

Calculating k Now, we perform the multiplication: ( − 3 ) × ( − 2 ) = 6 . Therefore, k = 6 .

Final Answer The constant of variation is k = 6 .


Examples
Inverse variation is a concept that shows up in many real-world situations. For example, the time it takes to complete a journey is inversely proportional to the speed at which you travel. If you double your speed, you halve the time it takes to arrive at your destination, assuming the distance stays the same. Similarly, in physics, the pressure of a gas is inversely proportional to its volume at a constant temperature. Understanding inverse variation helps us make predictions and understand relationships in various fields.

Answered by GinnyAnswer | 2025-07-04